As Dryden refused to report to the Bruins in 1964, they traded him to the Montreal Canadiens for Guy Allen and Paul Reid, two players who would never even make the NHL. Dryden made his NHL debut in mid-season 1971 for the Canadiens, and became the backbone of six Stanley Cup winning teams in 1971, 1973, 1976, 1977, 1978, and 1979. During that first playoff season, Dryden won the Conn Smythe Trophy (1971), as the playoffs' most valuable player. The following year Dryden won the Calder Trophy, 1972, as the Rookie of the year because the previous year he did not play enough regular season games to become eligible. He remains the only NHL player to ever win the Conn Smythe Trophy before winning the rookie of the year award. In the autumn of 1972 Dryden played for Team Canada in the 1972 Summit Series against the Soviet national ice hockey team.

Dryden played from 1971 to 1979, except for the 1973–74 season, when he was unhappy about the contract that the Canadiens offered him, which he considered less than his market worth, given that he had won the Stanley Cup and Vezina Trophy. He skipped training camp and held out that season, incurring the wrath of Canadiens General Manager Sam Pollock whose previous stars had usually signed for the amount that he had offered. Dryden used that year to fulfill the requirements for his law degree at McGill and article for a law firm. He retired following the 1978-79 season before he reached the age of 32.

Compared to most other goaltending greats, Dryden's NHL career was extremely short: only seven full seasons. Therefore, statistically he did not amass record totals in most categories. As he played all his years with a dynasty and retired before he could pass his prime, his statistical percentages are unparalleled. His regular season totals include a .790 winning percentage, a 2.24 goals against average, and, most incredibly, losing only 57 games while recording 46 shutouts in 397 total games. No other modern goaltender has ever been even remotely close to earning nearly as many shutouts as recording losing games. He won the Vezina Trophy five times for allowing the fewest goals and in the same years was selected as a First Team All-Star. Despite the comparative brevity of his career, in 1998, he was ranked number 25 on the List of 100 greatest hockey players by The Hockey News.

Dryden was so tall, at 6 foot 4 inches (193 cm), (and even taller on skates) that he was often seen during stoppages in play in what became his trademark pose: resting with his blocker propped up by his goalie stick which was angled to its maximum possible height. One of his nicknames was the "four-story goalie".

Minority owner Larry Tanenbaum hired Dryden to become the president of the Toronto Maple Leafs hockey club in 1997. Pat Quinn became head coach in 1998, and the two men reportedly had a frosty relationship. A few months after joining the Leafs, Quinn took on the General Manager position, reportedly to preempt Dryden from hiring his preferred GM which was former Habs teammate Bob Gainey.

On August 29, 2003, with the hiring of John Ferguson, Jr. as GM, there was a major management shakeup. Majority owner Steve Stavro was bought out by the Ontario Teachers' Pension Plan and he stepped down as chairman in favour of Larry Tanenbaum. Quinn continued as head coach but was relieved of GM duties. Dryden's position was abolished, in favour of having both the Leafs and Toronto Raptors managers reporting directly to MLSE President and CEO Richard Peddie. Dryden was shuffled to the less important role of vice-chairman and given a spot on MLSE's board of directors, which was described by commentators as "sitting outside the loop" as he did not report directly to Leafs ownership. He stayed on until 2004 when he resigned to enter politics.